That is LOUD!! I was going to suggest loose laminations in the motor, or even a loose stator coil, but that sounds for all the world like the noise a contactor makes rather than a motor, are you sure it is coming from the motor? has the contactor got the right voltage coil in it? the motor seems to run up to speed, and the cent sw sounds fine. Check that the centrifugal mechanmism has not moved on the shaft and is failing to open the contacts. The click you hear as the motor slows down is the centrifugal mechanism operating, not the switch contacts opening. as others have said, it does sound like the start winding is still in circuit, but louder than you would expect. Check the contactor if there is one.